Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have this problem on a past exam paper I am having some trouble with:

"in the conventional basis of the eigenstates of the S_{z}operator, the spin state of a spin-1/2 particle is described by the vector:

[tex] u = \left( \stackrel{cos a}{e^i^b sina} \right)[/tex] where a and B are constants.

find the probability that a measurement of the y-component of the spin of the particle will yield the result [tex] 0.5\hbar [/tex] ."

For the life of me I cannot work out how to write out matrices legibly on this thing, so I will summarize what is bothering me. I am given pauli matrices [tex] \sigma_x_,_y_,_z [/tex]that I cannot write out properly, and the spin operator is given by [tex] S_i = i\hbar\sigma_i [/tex].

In the question I am given the vector u, which is apparently expressed in the basis of S_{z}eigenstates.

Am I justified in putting this vector u into an eigenvalue equation [tex] S_{y} u = a_{y} u [/tex] ,

where a_{y}is my eigenvalue, when the vector I would be operating on is made from a basis of eigenstates of another operator (S_{z})?

I tried this and got two equations for a_{y}, neither of which gives [tex] a_y = 0.5\hbar [/tex].

does this mean I can conclude that there is zero probability of finding the y-component of the spin being equal to [tex] 0.5\hbar [/tex] ?

or do I somehow have to wangle it so that I get another vector (not u) that is in the S_{y}eigenstate basis?

thanks.

PS. sorry, this crazy thing will not let me change something 5 lines up where I should have said

"Am I justified in putting this vector u into an eigenvalue equation S_y u = 0.5\hbar u"

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Quantum mechanics - spin operator eigenvalue probability?

**Physics Forums | Science Articles, Homework Help, Discussion**